Gaseous viscous peeling of linearly elastic substrates

TL;DR

This paper investigates the complex interplay of elasticity, viscosity, and rarefaction in the pressure-driven flow of gas in micron-scale elastic gaps, providing self-similar solutions validated by numerical analysis.

Contribution

It introduces a unified framework for analyzing gaseous viscous peeling in elastic microchannels, accounting for multiple physical regimes and weak rarefaction effects.

Findings

Derived self-similar solutions for different physical regimes.

Identified symmetry between compressibility and elasticity effects.

Validated analytical solutions with numerical simulations.

Abstract

We study pressure-driven propagation of gas into a micron-scale gap between two linearly elastic substrates. Applying the lubrication approximation, the flow-field is governed by the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-compressibility, characteristic to gaseous microflows. Several physical limits allow simplification of the governing evolution equation and enable solution by self-similarity. These limits correspond to different time-scales and physical regimes which include compressiblity-elasticity-viscosity, compressiblity-viscosity and elasticity-viscosity dominant balances. For a prewetting layer thickness which is similar to the elastic deformation generated by the background pressure, a symmetry between compressibility and elasticity allows to obtain a self-similar solution which includes weak rarefaction effects. The results are validated by numerical solutions of the evolution equation